In [2]:
import geopandas as gpd
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np

pd.set_option('display.max_columns', 500)

Lab 4: Fire Service Coverage Analysis - Maximal Covering Location Problem¶

For this lab we return to Fire Service Coverage seeking to assess tradeoffs in service against costs of maintaining different levels of stations.
Instead of covering all demand, the modeling approach tries to maximize the demand covered.
Specifically, we will employ the maximal covering location problem.
Instead of minimizing the number of facilities needed in a previous lab, we now introduce a parameter, $p$, representing a fixed number of facilities to keep in the system.

In Lab 4, there are three research questions we want to look into.

  1. Does a change in demand representation impact the optimization results?
  2. How can a service system be evaluated to prioritize demand maximization?
  3. Can the analysis process be generalized in order to replicate the approach using different demand representations?

The coverage standard for this lab will be fixed at 8000m.

In [3]:
S = 8000

Step 1. Prepare your dataset¶

Task: Load the three datasets and convert blocks and stations crs into the same one as FDs.crs.¶

  • It is because FDs is in a crs using meter as linear unit.
In [4]:
# Note: it might take time, as FD is a huge file.

FDs = gpd.read_file("Data/California_Fire_Districts.shp") # load a shapefile containing California Fire District here
blocks = gpd.read_file("Data/sbBlocks_pop.shp") # Load a shapefile containing Santa Barbara County blocks here
stations = gpd.read_file("Data/Fire_Stations_SBC.shp") # Load a shapefile containing Fire Stations in Santa Barbara County here

Task: Look into the following Fire District maps.¶

There are many Fire Districts in California.
We are only going to focus in the "Santa Barbara County Fire District".
In the second map, note that there are many other Fire Districts in Santa Barbara County.
Though it's not shown on the map, they have some overlapping area, which means the area is co-operated by multiple Fire Districts.

In [5]:
blocks = blocks.to_crs("epsg:3310") 

stations = stations.to_crs("epsg:3310")
In [6]:
FDs.plot("Name")
Out[6]:
<Axes: >
No description has been provided for this image
In [7]:
FDs = FDs.loc[FDs.intersects(blocks.unary_union)].reset_index(drop=True)
FDs.plot("Name", legend=True, figsize=(10,10))
Out[7]:
<Axes: >
No description has been provided for this image

Question 1: Sort out a Fire District out of FDs GeoDataFrame. The district must have its 'Name" column value, "SANTA BARBARA CFD". ( 1 pt )¶

In [8]:
#FDs.crs
In [9]:
#blocks.crs
In [10]:
#stations.crs
In [11]:
FDs
Out[11]:
OBJECTID County FDID MACSID Name Address City Zip FireChief Phone Notes LastUpdate Website CALFIREUni SHAPE_Leng SHAPE_Area geometry
0 89 KERN 15010 KRN KERN CO FD 5642 VICTOR ST BAKERSFIELD 93308 AARON DUNCAN (661) 391‐7000 None 2018-06-21 https://kerncountyfire.org/ KRN 998841.649563 1.921083e+10 MULTIPOLYGON (((207559.325 -315382.144, 207622...
1 304 SAN LUIS OBISPO 40080 SLC SAN LUIS OBISPO CO FD 635 N SANTA ROSA ST SAN LUIS OBISPO 93405 JOHN OWENS (805) 543‐4244 None 2018-06-21 https://calfireslo.org/ SLU 940256.942591 8.344077e+09 MULTIPOLYGON (((-58528.672 -319737.906, -58473...
2 316 SANTA BARBARA 42005 CRP CARPINTERIA SUMMERLAND FPD 1140 EUGENE PLACE, SUITE A CARPINTERIA 93013 GREG FISH (805) 684‐4591 None 2018-06-21 https://www.carpfire.com/ SBC 49534.138992 1.010901e+08 POLYGON ((50973.663 -398386.099, 50969.942 -39...
3 317 SANTA BARBARA 42030 MTO MONTECITO FPD 595 SAN YSIDRO RD SANTA BARBARA 93108 KEVIN TAYLOR (805) 969‐7762 None 2018-06-21 https://www.montecitofire.com/ SBC 39911.074682 3.644463e+07 POLYGON ((35557.315 -399389.055, 35295.841 -39...
4 318 SANTA BARBARA 42035 SBC SANTA BARBARA CFD 4410 CATHEDRAL OAKS RD SANTA BARBARA 93110 MARK A. HARTWIG (805) 681‐5500 None 2018-06-21 https://www.sbcfire.com/ SBC 778360.396807 3.666998e+09 MULTIPOLYGON (((23728.804 -401033.857, 23715.3...
5 396 VENTURA 56020 VNC VENTURA COUNTY FPD 165 DURLEY AVE CAMARILLO 93010 DUSTIN GARDNER (805) 389‐9710 None 2018-06-21 https://vcfd.org/ VNC 840086.616548 4.239353e+09 MULTIPOLYGON (((72888.961 -429800.719, 72849.7...
6 647 SANTA BARBARA 42010 GUA GUADALUPE FD 918 OBISPO ST GUADALUPE 93434 MICHAEL CASH (805) 356‐3905 None 2022-02-10 https://ci.guadalupe.ca.us/fire/ SBC 14598.470583 3.446183e+06 POLYGON ((-52159.523 -337901.424, -52142.953 -...
7 662 SANTA BARBARA 42040 SMR SANTA MARIA FD 314 WEST COOK ST #8 SANTA MARIA 93458 TODD TUGGLE (805) 925‐0951 None 2022-02-14 https://www.cityofsantamaria.org/city-governme... SBC 71542.884890 6.075262e+07 MULTIPOLYGON (((-36710.959 -344913.125, -36707...
8 676 SANTA BARBARA 42025 STB SANTA BARBARA CITY FD 925 CHAPALA ST SANTA BARBARA 93101 CHRIS MAILES (805) 965‐5254 None 2022-02-14 https://www.santabarbaraca.gov/gov/depts/fire/... SBC 81431.348424 5.056587e+07 MULTIPOLYGON (((15469.272 -397501.519, 15472.5...
9 678 SANTA BARBARA 42015 LMP LOMPOC FD 115 SOUTH G ST LOMPOC 93436 BRIAN FALLON (805) 736‐4513 None 2022-02-14 https://www.cityoflompoc.com/government/depart... SBC 38950.291184 3.025921e+07 MULTIPOLYGON (((-42597.382 -377627.460, -42626...
In [12]:
SBC_FD = FDs.loc[FDs["Name"] == "SANTA BARBARA CFD"].reset_index() ##PUT YOUR ANSWER HERE##
In [13]:
SBC_FD
Out[13]:
index OBJECTID County FDID MACSID Name Address City Zip FireChief Phone Notes LastUpdate Website CALFIREUni SHAPE_Leng SHAPE_Area geometry
0 4 318 SANTA BARBARA 42035 SBC SANTA BARBARA CFD 4410 CATHEDRAL OAKS RD SANTA BARBARA 93110 MARK A. HARTWIG (805) 681‐5500 None 2018-06-21 https://www.sbcfire.com/ SBC 778360.396807 3.666998e+09 MULTIPOLYGON (((23728.804 -401033.857, 23715.3...
In [14]:
#SBC_FD.plot()

Task: Run following cell, "del FDs". Note: It will delete FDs variable.¶

We do this because FDs contains a large shapefile, which might burden your RAM.

In [15]:
del FDs

Task: take a subset of stations, within SBC_FD.¶

NOTE: don't forget to RESET_INDEX() whenever you take a subset!

In [16]:
stations
Out[16]:
Label Desig Number Type Department Name_other Address Notes Num_2019 Scale Latitude Longitude geometry
0 VAFB-41 AFV-1 41 Fire Station Vandenberg Fire Department None Airfield Rd., Vandenberg, CA None 41 0 34.7342 -120.569 POINT (-52075.698 -364541.170)
1 VAFB-42 AFV-2 42 Fire Station Vandenberg Fire Department None New Mexico Ave., Vandenberg, CA None 42 0 34.7345 -120.534 POINT (-48865.923 -364526.814)
2 VAFB-44 AFV-4 44 Fire Station Vandenberg Fire Department None Arguello Rd., Vandenberg, CA None 44 0 34.6125 -120.570 POINT (-52227.109 -378048.804)
3 VAFB-45 AFV-5 45 Fire Station Vandenberg Fire Department None Lasalle Canyon Rd., Vandenberg, CA None 45 0 34.6496 -120.614 POINT (-56277.374 -373901.714)
4 SBC-31 SBC-31 31 Fire Station Santa Barbara County Fire Department None 168 W Hwy 246, Buellton, CA 93427 None 31 900 34.6132 -120.197 POINT (-18043.064 -378107.359)
... ... ... ... ... ... ... ... ... ... ... ... ... ...
203 LAC-143 LAC-143 143 Fire Station LAC None None None None 0 34.4545 -118.634 POINT (125491.361 -394834.163)
204 VNC-Saticoy VNC-Saticoy 0 Fire Station VNC None None None None 0 34.3115 -119.134 POINT (79681.290 -411244.355)
205 VNC-27 VNC-27 27 Fire Station VNC None None None None 0 34.3935 -118.928 POINT (98577.520 -401948.877)
206 VNC-85 VNC-85 85 Fire Station VNC None None None None 0 34.1862 -118.930 POINT (98645.842 -424951.021)
207 KRN-58 KRN-58 58 Fire Station KRN None None None None 0 34.8523 -119.169 POINT (75904.018 -351258.013)

208 rows × 13 columns

In [17]:
stations = stations.loc[stations.within(SBC_FD.unary_union)].reset_index()
#stations.loc[stations["Department"].isin(["Santa Barbara County Fire Department"])].reset_index()
In [18]:
len(stations)
Out[18]:
28
In [19]:
len(blocks)
Out[19]:
7258

Question 2: Plot the blocks GeoDataFrame. ( 2 pts )¶

  • Firstly, update the blocks GeoDataFrame's geometry column to have block centroids, not block polygons ( 0.5 pt )
  • Secondly, take a subset of blocks which is within the SBC_FD area ( 0.5 pt )
  • Thirdly, plot blocks GeoDataFrame with "Population" column. ( 1 pt )
    • figsize=(10,10)
    • opacity must be 0.4
    • take a cmap (colormap) that you like from this webpage (https://matplotlib.org/stable/users/explain/colors/colormaps.html).
    • markersize must be proportional to the column, "Population"
    • ensure you have legend
    • Plot with stations GeoDataFrame

Hint: when there's something you don't know about plot function, refer to this document page (https://geopandas.org/en/stable/docs/reference/api/geopandas.GeoDataFrame.plot.html)! Also, you can Google or ask chatGPT :)

In [20]:
from matplotlib_scalebar.scalebar import ScaleBar
In [21]:
#blocks.centroid.plot(ax=A, markersize=blocks.elpop * 2, color="orange", label="Block Centroids")  

blocks["geometry"] = blocks["geometry"].centroid
In [22]:
#blocks
In [23]:
blocks = blocks.loc[blocks.within(SBC_FD.unary_union.buffer(10))].reset_index()
In [24]:
blocks["Population"].max()
Out[24]:
2598
In [25]:
blocks = blocks.loc[blocks["Population"] > 0].reset_index()
In [26]:
A = stations.plot(color="red", zorder = 10, markersize = 10)

blocks.plot("Population", legend=True, figsize=(10,10), ax=A, markersize=blocks["Population"]/2, cmap = "summer", alpha = 0.4)
plt.title("Block Population and Stations in Santa Barbara CFD")

scalebar = ScaleBar(dx=1, scale_formatter=lambda data, unit: f'{data}000 m', length_fraction=0.25)
A.add_artist(scalebar)
Out[26]:
<matplotlib_scalebar.scalebar.ScaleBar at 0x162357490>
No description has been provided for this image

Step 2. Conduct MCLP¶

Decision Variables: \begin{align*} & x_j = \begin{cases} 1, & \text{if facility $j$ is open}, \\ 0, & \text{otherwise}. \end{cases} \\ & y_i = \begin{cases} 1, & \text{if demand $i$ is covered}, \\ 0, & \text{otherwise}. \end{cases} \end{align*}

Parameters: \begin{align*} & I = \text{number of demands}, \\ & J = \text{number of facilities}, \\ & S = \text{Coverage Distance Standard}, \\ & a_i = \text{Weight assigned to demand $i$}, \\ & D_{ij} = \text{Distance between demand $i$ and facility $j$}, \\ & N_i = \{ j \in J \, | \, D_{ij} \leq S \}, \\ & P = \text{the number of facilities to be opened}. \end{align*}

Objective Function: \begin{align*} \text{Maximize:} \quad & \sum_{i=1}^{I} a_i y_i \end{align*}

Constraints: \begin{align*} \text{Subject to:} \quad & \sum_{j \in N_i} x_j \geq y_i, \quad \forall i \in I \\ & \sum_{j=1}^{J} x_j \leq P, \\ & x_j, y_i \in \{0, 1\}, \quad \forall i, j. \end{align*}

Task: Based on the mathematical Model, set the I and J values correctly.¶

  • In this section, we will consider each block as demand $i$
  • we will consider each existing fire station as facility $j$
  • In the beginning of this lab, we defined our S value to be 8000 meter, 8 km.
  • Pick any P that is less than current number of stations :)
In [27]:
I = len(blocks)
J = len (stations)
P = 20

Task: We are going to have block's population as weight assigned to demand. Define $a_i$.¶

In [28]:
a_i = blocks["Population"]

Task: Create $D_{ij}$ variable using Euclidean Distance between demand $i$ and facility $j$.¶

In [29]:
D_ij = [[np.sqrt((blocks.geometry.centroid.x[i] - stations.geometry.x[j])**2 + (blocks.geometry.centroid.y[i] - stations.geometry.y[j])**2)
         for j in range(J)] for i in range (I)]

Question 3: Create $N_i$ variable in list format. ( 1 pt )¶

  • Previously, $N_i$ in dictionary is introduced.
  • With your understanding so far, list format of $N_i$ can also be created.
  • You can use double for-loops, or list comprehension.
In [30]:
# This is a hint for students who want to do it with list comprehension


# Creating a two-dimensional list
matrix = [[1, 2, 3],
          [4, 5, 6],
          [7, 8, 9],
          [10, 11, 12]]

# Using list comprehension to filter even numbers from the matrix
# The '%' symbol in Python is called the modulo operator. 
    #It returns the remainder of the division of the left operand by the right operand.
even_numbers = [[matrix[r][c] for c in range(len(matrix[0])) if matrix[r][c]%2 == 0]
                for r in range(len(matrix))]

print(even_numbers)

[[2], [4, 6], [8], [10, 12]]
In [32]:
np.array(D_ij).shape, (I,J)
Out[32]:
((1965, 28), (1965, 28))
In [33]:
D_ij = np.array(D_ij)
In [34]:
N_i = [[j for j in range(len(D_ij[0])) if D_ij[i, j] <= 8000]
       for i in range (len(D_ij))]
In [35]:
#N_i

Question 4: Complete the Optimization Model ( 6 pts )¶

In [36]:
import gurobipy as gp
from gurobipy import GRB

# Create a new Gurobi model
mclp = gp.Model("Maximal_Covering_Location")

# Decision Variables
x = mclp.addVars(J, vtype=GRB.BINARY, name="x")  # Facility is open or not
y = mclp.addVars(I, vtype=GRB.BINARY, name="y")   # Demand is covered or not

# Objective Function
mclp.setObjective((gp.quicksum(a_i[i] * y[i] for i in range (I))), GRB.MAXIMIZE)

# Constraints
# Each demand must be covered by neighboring facility
mclp.addConstrs((gp.quicksum(x[j] for j in N_i[i]) >= y[i] for i in range(I)))


# Number of opened facilities must not exceed P
mclp.addConstr((gp.quicksum(x[j] for j in range(J))) == P)

# Optimize the model
mclp.optimize()

Set parameter Username
Academic license - for non-commercial use only - expires 2025-05-10
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x6f090930
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 128757.00000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.01s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 167416.00000

Root relaxation: objective 1.676190e+05, 8 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167619.00000 167619.000  0.00%     -    0s

Explored 1 nodes (8 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167619 167416 128757 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676190000000e+05, best bound 1.676190000000e+05, gap 0.0000%

Question 5: Take a subset of stations based on the model output. ( 1 pt )¶

In [37]:
stations["selected"] = [x[j].x > 0.5 for j in range(len(stations))]
open_stations = stations.loc[stations["selected"]].reset_index(drop=True)
In [38]:
len(open_stations)
Out[38]:
20

Question 6: Plot the open_stations and their coverage buffers with the demand buffers. ( 2 pts )¶

  • Copy and Paste the plotting code from Question 2.
  • Replace stations with open_stations.
  • Add another plot function which plots the buffer with buffer distance S from each open_station.
    • The coverage buffer shouldn't have facecolor
    • Buffer Boundary must be dashed lines. (ask chatGPT of google how to do this!)
In [39]:
A = open_stations.plot(color="red", zorder = 10, markersize = 10)
open_stations.buffer(S).plot(ax=A, edgecolor="red", facecolor="None", linestyle="dashed")

blocks.plot("Population", legend=True, figsize=(10,10), ax=A, markersize=blocks["Population"]/2, cmap = "summer", alpha = 0.4)
plt.title("Block Population and Stations in Santa Barbara CFD")

scalebar = ScaleBar(dx=1, scale_formatter=lambda data, unit: f'{data}000 m', length_fraction=0.25)
A.add_artist(scalebar)
Out[39]:
<matplotlib_scalebar.scalebar.ScaleBar at 0x168d6fc90>
No description has been provided for this image

Step 3. Functionize / Modularize¶

Here, we will functionize our optimization model.
Sothat with given P value, the model can be solved.

Question 7: Functionize your code out of Question 4 and 5 ( 2 pts )¶

  • start defining a function named, "solve_mclp". ( 0.5 pts )
  • The function takes one argument, P. ( 0.5 pts )
  • Within the function, copy and paste the code you did for Question 4 and 5. ( 0.5 pts )
  • Then, add the last line of code, to return open_stations, and mclp.obj_val ( 0.5 pts )
In [40]:
# Let me give you functionize example.
# For more, refer to Lab 0.

sample_list = [1,2,3,4]

def sum_array(a):
    s = 0
    a = np.array(a)
    for num in a:
        s += num
    return s, a # Return the summation of all elements, and the original array

sum_array(sample_list)
Out[40]:
(10, array([1, 2, 3, 4]))
In [41]:
## PUT YOUR FUNCTION HERE!!!##

def solve_mclp(P):
    P = P
    import gurobipy as gp
    from gurobipy import GRB

    # Create a new Gurobi model
    mclp = gp.Model("Maximal_Covering_Location")

    # Decision Variables
    x = mclp.addVars(J, vtype=GRB.BINARY, name="x")  # Facility is open or not
    y = mclp.addVars(I, vtype=GRB.BINARY, name="y")   # Demand is covered or not

    # Objective Function
    mclp.setObjective((gp.quicksum(a_i[i] * y[i] for i in range (I))), GRB.MAXIMIZE)

    # Constraints
    # Each demand must be covered by neighboring facility
    mclp.addConstrs((gp.quicksum(x[j] for j in N_i[i]) >= y[i] for i in range(I)))


    # Number of opened facilities must not exceed P
    mclp.addConstr((gp.quicksum(x[j] for j in range(J))) == P)

    # Optimize the model
    mclp.optimize()
    
    stations["selected"] = [x[j].x > 0.5 for j in range(len(stations))]
    open_stations = stations.loc[stations["selected"]].reset_index(drop=True)


    return open_stations, mclp.obj_val

#solve_mclp(5)

Step 4. Evaluate the Result¶

Question 8: To evaluate the optimization result, we always compare with the current operation. Calculate current_coverage. ( 2 pts )¶

Current coverage is the sum of all the demand weights, currently covered by existing stations.
Here are the thought process you can go through.

  • Create buffers with distance S out of all the existing stations.
  • Take a unary_union of the buffers. ( 0.5 pts )
  • Use .within() function to take a subset of blocks, within the unary_union of coverage buffers. ( 0.5 pts )
  • Take the Population column out of the subset of blocks. ( 0.5 pts )
  • Take the sum of the column values. ( 0.5 pts )
In [42]:
stations_coverage = stations.buffer(S)

total_stations_coverage = stations_coverage.unary_union

blocks_within_coverage = blocks[blocks.geometry.within(total_stations_coverage)]

population_subset = blocks_within_coverage['Population']

current_coverage = population_subset.sum()

current_coverage
Out[42]:
167619

Task: Check if provided code works with your defined function, solve_mclp¶

In [43]:
selecteds = []  # List to store selected stations for each value of p
obj_vals = []   # List to store objective values for each value of p

# Iterate over values of p starting from 3
for p in range(3, len(stations)+1):
    print(f"=================== for P={p}")  # Print current value of p
    # Call solve_mclp function to solve the problem for current value of p
    selected_stations, obj_val = solve_mclp(p)
    # Append selected stations to the selecteds list
    selecteds.append(selected_stations)
    # Append objective value to the obj_vals list
    obj_vals.append(obj_val)

=================== for P=3
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0xe8181d39
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective 92175.000000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 94338.000000

Root relaxation: objective 1.420590e+05, 36 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    142059.00000 142059.000  0.00%     -    0s

Explored 1 nodes (36 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 142059 94338 92175 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.420590000000e+05, best bound 1.420590000000e+05, gap 0.0000%
=================== for P=4
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x0162568a
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective 92175.000000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 129507.00000

Root relaxation: objective 1.536120e+05, 33 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    153612.00000 153612.000  0.00%     -    0s

Explored 1 nodes (33 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 153612 129507 92175 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.536120000000e+05, best bound 1.536120000000e+05, gap 0.0000%
=================== for P=5
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x31882cce
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective 93253.000000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 130073.00000

Root relaxation: objective 1.578840e+05, 28 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    157884.00000 157884.000  0.00%     -    0s

Explored 1 nodes (28 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 157884 130073 93253 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.578840000000e+05, best bound 1.578840000000e+05, gap 0.0000%
=================== for P=6
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x72cbbd19
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective 93491.000000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 130311.00000

Root relaxation: objective 1.615770e+05, 26 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    161577.00000 161577.000  0.00%     -    0s

Explored 1 nodes (26 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 161577 130311 93491 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.615770000000e+05, best bound 1.615770000000e+05, gap 0.0000%
=================== for P=7
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0xed8b0a7b
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective 93491.000000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 145336.00000

Root relaxation: objective 1.637110e+05, 23 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    163711.00000 163711.000  0.00%     -    0s

Explored 1 nodes (23 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 163711 145336 93491 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.637110000000e+05, best bound 1.637110000000e+05, gap 0.0000%
=================== for P=8
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x6fba2f2b
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective 108080.00000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 145576.00000

Root relaxation: objective 1.657080e+05, 24 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    165708.00000 165708.000  0.00%     -    0s

Explored 1 nodes (24 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 165708 145576 108080 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.657080000000e+05, best bound 1.657080000000e+05, gap 0.0000%
=================== for P=9
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x7035f7b6
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective 119589.00000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 156952.00000

Root relaxation: objective 1.663460e+05, 24 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    166346.00000 166346.000  0.00%     -    0s

Explored 1 nodes (24 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 166346 156952 119589 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.663460000000e+05, best bound 1.663460000000e+05, gap 0.0000%
=================== for P=10
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0xd11c01cd
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 119589.00000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 157042.00000

Root relaxation: objective 1.669120e+05, 19 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    166912.00000 166912.000  0.00%     -    0s

Explored 1 nodes (19 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 166912 157042 119589 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.669120000000e+05, best bound 1.669120000000e+05, gap 0.0000%
=================== for P=11
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x7af76ba8
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 119589.00000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 157074.00000

Root relaxation: objective 1.671520e+05, 18 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167152.00000 167152.000  0.00%     -    0s

Explored 1 nodes (18 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167152 157074 119589 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.671520000000e+05, best bound 1.671520000000e+05, gap 0.0000%
=================== for P=12
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x4fa1b3b5
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 119658.00000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 157103.00000

Root relaxation: objective 1.673460e+05, 10 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167346.00000 167346.000  0.00%     -    0s

Explored 1 nodes (10 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167346 157103 119658 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.673460000000e+05, best bound 1.673460000000e+05, gap 0.0000%
=================== for P=13
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x1729feb8
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 125468.00000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 162548.00000

Root relaxation: objective 1.674650e+05, 10 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167465.00000 167465.000  0.00%     -    0s

Explored 1 nodes (10 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167465 162548 125468 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.674650000000e+05, best bound 1.674650000000e+05, gap 0.0000%
=================== for P=14
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x27935a42
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 126106.00000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 162548.00000

Root relaxation: objective 1.675350e+05, 8 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167535.00000 167535.000  0.00%     -    0s

Explored 1 nodes (8 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167535 162548 126106 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.675350000000e+05, best bound 1.675350000000e+05, gap 0.0000%
=================== for P=15
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x4d7e2f36
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 128228.00000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 163186.00000

Root relaxation: objective 1.676040e+05, 4 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167604.00000 167604.000  0.00%     -    0s

Explored 1 nodes (4 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167604 163186 128228 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676040000000e+05, best bound 1.676040000000e+05, gap 0.0000%
=================== for P=16
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0xc1d2ab13
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 128336.00000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 163186.00000

Root relaxation: objective 1.676180e+05, 5 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167618.00000 167618.000  0.00%     -    0s

Explored 1 nodes (5 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167618 163186 128336 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676180000000e+05, best bound 1.676180000000e+05, gap 0.0000%
=================== for P=17
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0xaeb6fde8
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 128365.00000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 166879.00000

Root relaxation: objective 1.676190e+05, 4 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167619.00000 167619.000  0.00%     -    0s

Explored 1 nodes (4 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167619 166879 128365 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676190000000e+05, best bound 1.676190000000e+05, gap 0.0000%
=================== for P=18
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0xc9f32491
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 128365.00000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 166879.00000

Root relaxation: objective 1.676190e+05, 4 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167619.00000 167619.000  0.00%     -    0s

Explored 1 nodes (4 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167619 166879 128365 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676190000000e+05, best bound 1.676190000000e+05, gap 0.0000%
=================== for P=19
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x32d7c1da
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 128687.00000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 167402.00000

Root relaxation: objective 1.676190e+05, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167619.00000 167619.000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167619 167402 128687 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676190000000e+05, best bound 1.676190000000e+05, gap 0.0000%
=================== for P=20
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x6f090930
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 128757.00000
Presolve removed 1928 rows and 1929 columns
Presolve time: 0.00s
Presolved: 38 rows, 64 columns, 195 nonzeros
Variable types: 0 continuous, 64 integer (63 binary)
Found heuristic solution: objective 167416.00000

Root relaxation: objective 1.676190e+05, 8 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167619.00000 167619.000  0.00%     -    0s

Explored 1 nodes (8 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167619 167416 128757 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676190000000e+05, best bound 1.676190000000e+05, gap 0.0000%
=================== for P=21
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0xac483780
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 128757.00000
Presolve removed 1929 rows and 1930 columns
Presolve time: 0.00s
Presolved: 37 rows, 63 columns, 186 nonzeros
Variable types: 0 continuous, 63 integer (62 binary)
Found heuristic solution: objective 167133.00000

Root relaxation: objective 1.676190e+05, 9 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167619.00000 167619.000  0.00%     -    0s

Explored 1 nodes (9 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167619 167133 128757 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676190000000e+05, best bound 1.676190000000e+05, gap 0.0000%
=================== for P=22
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x7f56a9df
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 132450.00000
Presolve removed 1931 rows and 1933 columns
Presolve time: 0.00s
Presolved: 35 rows, 60 columns, 164 nonzeros
Variable types: 0 continuous, 60 integer (58 binary)
Found heuristic solution: objective 167485.00000

Root relaxation: objective 1.676190e+05, 9 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167619.00000 167619.000  0.00%     -    0s

Explored 1 nodes (9 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 167619 167485 132450 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676190000000e+05, best bound 1.676190000000e+05, gap 0.0000%
=================== for P=23
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x2c5ff2db
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 132450.00000
Presolve removed 1934 rows and 1938 columns
Presolve time: 0.00s
Presolved: 32 rows, 55 columns, 138 nonzeros
Variable types: 0 continuous, 55 integer (52 binary)
Found heuristic solution: objective 167618.00000

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 167618 132450 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676180000000e+05, best bound 1.676190000000e+05, gap 0.0006%
=================== for P=24
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0xca8093f1
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 132451.00000
Presolve removed 1938 rows and 1943 columns
Presolve time: 0.00s
Presolved: 28 rows, 50 columns, 116 nonzeros
Variable types: 0 continuous, 50 integer (47 binary)
Found heuristic solution: objective 167619.00000

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 167619 132451 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676190000000e+05, best bound 1.676190000000e+05, gap 0.0000%
=================== for P=25
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x47935a47
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 132936.00000
Presolve removed 1966 rows and 1993 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167619 132936 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676190000000e+05, best bound 1.676190000000e+05, gap 0.0000%
=================== for P=26
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0xfd04765c
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective 165598.00000
Presolve removed 1966 rows and 1993 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167619 165598 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676190000000e+05, best bound 1.676190000000e+05, gap 0.0000%
=================== for P=27
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x82e57cf4
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective 165598.00000
Presolve removed 1966 rows and 1993 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 167619 165598 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676190000000e+05, best bound 1.676190000000e+05, gap 0.0000%
=================== for P=28
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1966 rows, 1993 columns and 8810 nonzeros
Model fingerprint: 0x91f973c1
Variable types: 0 continuous, 1993 integer (1993 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective 167619.00000
Presolve removed 1966 rows and 1993 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 1: 167619 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676190000000e+05, best bound 1.676190000000e+05, gap 0.0000%

Task: Check if the output Table is plausible. And learn how to create a pandas DataFrame¶

  • To create a DataFrame, you can call pandas.DataFrame() and deliver a dictionary.
  • The dictionary will have key and value pairs.
    • key will be the column name
    • value will be an array of column values
In [44]:
results = pd.DataFrame({
    'P': range(3, len(stations)+1),
    'Coverage': obj_vals
})
results
Out[44]:
P Coverage
0 3 142059.0
1 4 153612.0
2 5 157884.0
3 6 161577.0
4 7 163711.0
5 8 165708.0
6 9 166346.0
7 10 166912.0
8 11 167152.0
9 12 167346.0
10 13 167465.0
11 14 167535.0
12 15 167604.0
13 16 167618.0
14 17 167619.0
15 18 167619.0
16 19 167619.0
17 20 167619.0
18 21 167619.0
19 22 167619.0
20 23 167618.0
21 24 167619.0
22 25 167619.0
23 26 167619.0
24 27 167619.0
25 28 167619.0
In [45]:
def scatterplot_result(results):
    # Plot the DataFrame, in scatter plot, taking P values as x and Coverage values as y
    results.plot(kind="scatter", x="P", y="Coverage")
    # Add grid lines
    plt.grid(True)
    # Add the current coverage point in color red
    plt.scatter(len(stations), current_coverage, color="red")
    # provide a dashed red line to inform current coverage
    plt.axhline(y=current_coverage, color='r', linestyle='--', label='Current Coverage')
    # show the plot!
    plt.show()
    
scatterplot_result(results)
No description has been provided for this image

Task: Put your code to plot open_stations and coverage buffer from Question 6.¶

Feel free to edit any other plotting details

In [46]:
def map_result(p, demand_block=True):
    open_stations = selecteds[p-3]
    ## PUT YOUR ANSWER HERE ##

    A = open_stations.plot(color="red", zorder = 10, markersize = 10)
    open_stations.buffer(S).plot(ax=A, edgecolor="red", facecolor="None", linestyle="dashed")

    blocks.plot("Population", legend=True, figsize=(10,10), ax=A, markersize=blocks["Population"]/2, cmap = "summer", alpha = 0.4)
    plt.title("Block Population and Stations in Santa Barbara CFD")

    scalebar = ScaleBar(dx=1, scale_formatter=lambda data, unit: f'{data}000 m', length_fraction=0.25)
    A.add_artist(scalebar)
    
    if demand_block:
        blocks.plot("Population", ax=A, legend=True, markersize=5)
    else:
        fishnet_points.plot(ax=A)
    plt.title(f"{p} stations open")
    plt.show()
    
map_result(14) # Try different p!
No description has been provided for this image

Task: Following function is to go through the whole process. Check if you get the same output as before :)¶

In [47]:
def optimize_and_evaluate(demand_block=True):
    selecteds = [] 
    obj_vals = [] 
    for p in range(3, len(stations)+1):
        print(f"=================== for P={p}")
        selected_stations, obj_val = solve_mclp(p)
        selecteds.append(selected_stations)
        obj_vals.append(obj_val)
        map_result(p, demand_block)
        
    results = pd.DataFrame({
        'P': range(3, len(stations)+1),
        'Coverage': obj_vals
    })
    scatterplot_result(results)
In [69]:
optimize_and_evaluate()

=================== for P=3
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xcef4b780
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective 13.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 43.0000000

Root relaxation: objective 8.600000e+01, 39 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0      86.0000000   86.00000  0.00%     -    0s

Explored 1 nodes (39 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 86 43 13 

Optimal solution found (tolerance 1.00e-04)
Best objective 8.600000000000e+01, best bound 8.600000000000e+01, gap 0.0000%
No description has been provided for this image 
=================== for P=4
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x6c1b8065
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective 13.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 67.0000000

Root relaxation: objective 1.130000e+02, 35 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     113.0000000  113.00000  0.00%     -    0s

Explored 1 nodes (35 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 113 67 13 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.130000000000e+02, best bound 1.130000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=5
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x0edd7bb0
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective 39.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 86.0000000

Root relaxation: objective 1.380000e+02, 33 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     138.0000000  138.00000  0.00%     -    0s

Explored 1 nodes (33 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 138 86 39 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.380000000000e+02, best bound 1.380000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=6
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x7ec0d3f0
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective 64.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 111.0000000

Root relaxation: objective 1.610000e+02, 35 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     161.0000000  161.00000  0.00%     -    0s

Explored 1 nodes (35 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 161 111 64 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.610000000000e+02, best bound 1.610000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=7
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xc0c56a2c
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective 67.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 114.0000000

Root relaxation: objective 1.840000e+02, 29 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     184.0000000  184.00000  0.00%     -    0s

Explored 1 nodes (29 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 184 114 67 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.840000000000e+02, best bound 1.840000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=8
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x42f51dea
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective 95.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 138.0000000

Root relaxation: objective 2.040000e+02, 22 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     204.0000000  204.00000  0.00%     -    0s

Explored 1 nodes (22 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 204 138 95 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.040000000000e+02, best bound 2.040000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=9
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xa05648d8
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective 119.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 169.0000000

Root relaxation: objective 2.210000e+02, 26 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     221.0000000  221.00000  0.00%     -    0s

Explored 1 nodes (26 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 221 169 119 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.210000000000e+02, best bound 2.210000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=10
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x9694b029
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 119.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 182.0000000

Root relaxation: objective 2.360000e+02, 22 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     236.0000000  236.00000  0.00%     -    0s

Explored 1 nodes (22 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 236 182 119 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.360000000000e+02, best bound 2.360000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=11
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x53e70d3e
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 120.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 208.0000000

Root relaxation: objective 2.480000e+02, 23 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     248.0000000  248.00000  0.00%     -    0s

Explored 1 nodes (23 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 248 208 120 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.480000000000e+02, best bound 2.480000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=12
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xde16faa2
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 131.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 212.0000000

Root relaxation: objective 2.600000e+02, 20 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     260.0000000  260.00000  0.00%     -    0s

Explored 1 nodes (20 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 260 212 131 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.600000000000e+02, best bound 2.600000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=13
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x2e87b538
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 144.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 221.0000000

Root relaxation: objective 2.710000e+02, 14 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     271.0000000  271.00000  0.00%     -    0s

Explored 1 nodes (14 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 271 221 144 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.710000000000e+02, best bound 2.710000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=14
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xe773f88b
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 161.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 244.0000000

Root relaxation: objective 2.750000e+02, 13 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     275.0000000  275.00000  0.00%     -    0s

Explored 1 nodes (13 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 275 244 161 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.750000000000e+02, best bound 2.750000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=15
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xf376824c
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 188.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 255.0000000

Root relaxation: objective 2.780000e+02, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     278.0000000  278.00000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 278 255 188 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.780000000000e+02, best bound 2.780000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=16
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x34bf2713
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 200.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 268.0000000

Root relaxation: objective 2.800000e+02, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     280.0000000  280.00000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 280 268 200 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.800000000000e+02, best bound 2.800000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=17
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x2fae766a
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 201.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 271.0000000

Root relaxation: objective 2.820000e+02, 9 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     282.0000000  282.00000  0.00%     -    0s

Explored 1 nodes (9 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 282 271 201 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.820000000000e+02, best bound 2.820000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=18
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xaef0dd05
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 201.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 271.0000000

Root relaxation: objective 2.830000e+02, 4 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     283.0000000  283.00000  0.00%     -    0s

Explored 1 nodes (4 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 283 271 201 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=19
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xeb12e722
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 202.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 270.0000000

Root relaxation: objective 2.830000e+02, 5 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     283.0000000  283.00000  0.00%     -    0s

Explored 1 nodes (5 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 283 270 202 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=20
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xdcf615d7
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 217.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 281.0000000

Root relaxation: objective 2.830000e+02, 5 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     283.0000000  283.00000  0.00%     -    0s

Explored 1 nodes (5 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 283 281 217 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=21
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xbec14725
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 217.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 282.0000000

Root relaxation: objective 2.830000e+02, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     283.0000000  283.00000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 283 282 217 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=22
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x7000900b
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 243.0000000
Presolve removed 487 rows and 491 columns
Presolve time: 0.00s
Presolved: 32 rows, 55 columns, 137 nonzeros
Variable types: 0 continuous, 55 integer (52 binary)
Found heuristic solution: objective 282.0000000

Root relaxation: objective 2.830000e+02, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     283.0000000  283.00000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 283 282 243 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=23
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x6558704c
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 243.0000000
Presolve removed 488 rows and 493 columns
Presolve time: 0.00s
Presolved: 31 rows, 53 columns, 130 nonzeros
Variable types: 0 continuous, 53 integer (50 binary)
Found heuristic solution: objective 282.0000000

Root relaxation: objective 2.830000e+02, 5 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     283.0000000  283.00000  0.00%     -    0s

Explored 1 nodes (5 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 283 282 243 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=24
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x2ed23144
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 244.0000000
Presolve removed 490 rows and 496 columns
Presolve time: 0.00s
Presolved: 29 rows, 50 columns, 119 nonzeros
Variable types: 0 continuous, 50 integer (47 binary)
Found heuristic solution: objective 283.0000000

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 283 244 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=25
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x4c00ff32
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 257.0000000
Presolve removed 519 rows and 546 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 283 257 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=26
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xd21c0cfb
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective 277.0000000
Presolve removed 519 rows and 546 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 283 277 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=27
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x9811cf51
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective 277.0000000
Presolve removed 519 rows and 546 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 283 277 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=28
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xae7d1ec3
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective 283.0000000
Presolve removed 519 rows and 546 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 1: 283 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image
No description has been provided for this image

¶

Step 4. Replicate your Analysis with different Demand Representations

Task: Review from Lab 2. We are creating fishnet points within the SBC_FD¶

In [49]:
boundary = SBC_FD.envelope # .envelope gives you the bounding rectangle of given GeoDataFrame.
boundary.bounds
Out[49]:
minx miny maxx maxy
0 -61331.613 -401270.1778 50847.5684 -323367.7559
In [50]:
minx, miny, maxx, maxy = boundary.loc[0].bounds
print(minx, miny, maxx, maxy)

-61331.61300000176 -401270.1777999997 50847.56839999929 -323367.7559000002
In [51]:
from shapely.geometry import Point

# Here, we are going to create fishnet points.
    # Fishnet points are points spaced with an equal interval.
    # You'll see when you see the output!

# Define the interval between points 
#### Note: Adjust interval value as needed for lab question 2
def create_fishnet(interval):
# Create arrays of x and y coordinates using np.arange
    x_coords = np.arange(minx, maxx, interval)
    y_coords = np.arange(miny, maxy, interval)

    # Create a list to store the points
    fishnet_points = []

    # Generate points for the fishnet
    for y in y_coords:
        for x in x_coords:
            fishnet_points.append((x, y))

    # Print the number of points generated
    print("Number of points in the fishnet:", len(fishnet_points))

    fishnet_points = gpd.GeoSeries([Point(pt_cd) for pt_cd in fishnet_points])
    fishnet_points = fishnet_points[fishnet_points.within(SBC_FD.geometry[0])].reset_index()
    fishnet_points.plot(figsize=(15,5))
    return fishnet_points
In [52]:
interval = 5280/5  # default: 5280/5 feet (1 mile / 5 = 0.2 mile) 
fishnet_points = create_fishnet(interval)

Number of points in the fishnet: 7918
No description has been provided for this image
In [53]:
# Current Coverage
current_coverage = fishnet_points.within(stations.buffer(S).unary_union).sum()

Question 9: Re-compute the model variables here for fishnet_points, instead of blocks. ( 1 pt )¶

Note: all the fishnet points will have the same weight, 1.

In [54]:
fishnet_points["weight"] = 1
In [55]:
I = len(fishnet_points)
J = len(stations)
a_i = fishnet_points["weight"]

D_ij = [[np.sqrt((fishnet_points.geometry.x[i] - stations.geometry.x[j])**2 + (fishnet_points.geometry.y[i] - stations.geometry.y[j])**2)
         for j in range(J)] for i in range (I)]

N_i = [[j for j in range(len(D_ij[0])) if D_ij[i][j] <= 8000]
       for i in range (len(D_ij))]
In [56]:
#fishnet_points.geometry
In [57]:
#fishnet_points.x
In [59]:
#fishnet_points
In [60]:
optimize_and_evaluate(demand_block=False)

=================== for P=3
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xe9047901
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective 103.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 289.0000000

Root relaxation: objective 5.400000e+02, 54 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     540.0000000  540.00000  0.00%     -    0s

Explored 1 nodes (54 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 540 289 103 

Optimal solution found (tolerance 1.00e-04)
Best objective 5.400000000000e+02, best bound 5.400000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=4
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x5c151c55
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective 103.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 446.0000000

Root relaxation: objective 7.040000e+02, 55 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     704.0000000  704.00000  0.00%     -    0s

Explored 1 nodes (55 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 704 446 103 

Optimal solution found (tolerance 1.00e-04)
Best objective 7.040000000000e+02, best bound 7.040000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=5
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x30b1d761
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective 272.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 564.0000000

Root relaxation: objective 8.550000e+02, 56 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     855.0000000  855.00000  0.00%     -    0s

Explored 1 nodes (56 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 855 564 272 

Optimal solution found (tolerance 1.00e-04)
Best objective 8.550000000000e+02, best bound 8.550000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=6
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x4d618f48
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective 433.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 725.0000000

Root relaxation: objective 1.005000e+03, 45 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1005.0000000 1005.00000  0.00%     -    0s

Explored 1 nodes (45 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1005 725 433 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.005000000000e+03, best bound 1.005000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=7
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x86f835a6
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective 450.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 891.0000000

Root relaxation: objective 1.146000e+03, 40 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1146.0000000 1146.00000  0.00%     -    0s

Explored 1 nodes (40 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1146 891 450 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.146000000000e+03, best bound 1.146000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=8
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xd0acb5e1
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective 631.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 1045.0000000

Root relaxation: objective 1.270000e+03, 40 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1270.0000000 1270.00000  0.00%     -    0s

Explored 1 nodes (40 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1270 1045 631 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.270000000000e+03, best bound 1.270000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=9
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xfab77a07
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective 780.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 1143.0000000

Root relaxation: objective 1.384000e+03, 34 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1384.0000000 1384.00000  0.00%     -    0s

Explored 1 nodes (34 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1384 1143 780 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.384000000000e+03, best bound 1.384000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=10
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x7479a8cc
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 780.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 1227.0000000

Root relaxation: objective 1.475000e+03, 35 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1475.0000000 1475.00000  0.00%     -    0s

Explored 1 nodes (35 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1475 1227 780 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.475000000000e+03, best bound 1.475000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=11
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x8bfbba92
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 790.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 1293.0000000

Root relaxation: objective 1.564000e+03, 32 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1564.0000000 1564.00000  0.00%     -    0s

Explored 1 nodes (32 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1564 1293 790 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.564000000000e+03, best bound 1.564000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=12
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xf70b3ac7
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 858.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 1407.0000000

Root relaxation: objective 1.647000e+03, 32 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1647.0000000 1647.00000  0.00%     -    0s

Explored 1 nodes (32 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1647 1407 858 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.647000000000e+03, best bound 1.647000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=13
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xe1965031
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 945.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 1376.0000000

Root relaxation: objective 1.715000e+03, 21 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1715.0000000 1715.00000  0.00%     -    0s

Explored 1 nodes (21 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1715 1376 945 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.715000000000e+03, best bound 1.715000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=14
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x71c262ee
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 1059.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 1490.0000000

Root relaxation: objective 1.743000e+03, 22 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1743.0000000 1743.00000  0.00%     -    0s

Explored 1 nodes (22 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1743 1490 1059 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.743000000000e+03, best bound 1.743000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=15
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x0af939ff
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 1230.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 1499.0000000

Root relaxation: objective 1.763000e+03, 21 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1763.0000000 1763.00000  0.00%     -    0s

Explored 1 nodes (21 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1763 1499 1230 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.763000000000e+03, best bound 1.763000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=16
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x0b49ef42
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 1310.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 1567.0000000

Root relaxation: objective 1.780000e+03, 16 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1780.0000000 1780.00000  0.00%     -    0s

Explored 1 nodes (16 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1780 1567 1310 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.780000000000e+03, best bound 1.780000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=17
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x526d2816
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 1313.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 1571.0000000

Root relaxation: objective 1.789000e+03, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1789.0000000 1789.00000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1789 1571 1313 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.789000000000e+03, best bound 1.789000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=18
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x03da43ef
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 1313.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 1571.0000000

Root relaxation: objective 1.793000e+03, 9 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1793.0000000 1793.00000  0.00%     -    0s

Explored 1 nodes (9 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1793 1571 1313 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.793000000000e+03, best bound 1.793000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=19
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xc8613c39
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 1317.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 1573.0000000

Root relaxation: objective 1.797000e+03, 4 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1797.0000000 1797.00000  0.00%     -    0s

Explored 1 nodes (4 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1797 1573 1317 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=20
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xd2fb92d6
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 1408.0000000
Presolve removed 3254 rows and 3254 columns
Presolve time: 0.00s
Presolved: 51 rows, 78 columns, 253 nonzeros
Variable types: 0 continuous, 78 integer (78 binary)
Found heuristic solution: objective 1641.0000000

Root relaxation: objective 1.797000e+03, 4 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1797.0000000 1797.00000  0.00%     -    0s

Explored 1 nodes (4 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1797 1641 1408 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=21
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xefd84af8
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 1408.0000000
Presolve removed 3255 rows and 3255 columns
Presolve time: 0.00s
Presolved: 50 rows, 77 columns, 244 nonzeros
Variable types: 0 continuous, 77 integer (77 binary)
Found heuristic solution: objective 1772.0000000

Root relaxation: objective 1.797000e+03, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1797.0000000 1797.00000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1797 1772 1408 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=22
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xefb7c4b9
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 1563.0000000
Presolve removed 3257 rows and 3257 columns
Presolve time: 0.00s
Presolved: 48 rows, 75 columns, 228 nonzeros
Variable types: 0 continuous, 75 integer (75 binary)
Found heuristic solution: objective 1792.0000000

Root relaxation: objective 1.797000e+03, 8 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1797.0000000 1797.00000  0.00%     -    0s

Explored 1 nodes (8 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1797 1792 1563 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=23
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x7e54be92
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 1563.0000000
Presolve removed 3261 rows and 3263 columns
Presolve time: 0.00s
Presolved: 44 rows, 69 columns, 192 nonzeros
Variable types: 0 continuous, 69 integer (68 binary)
Found heuristic solution: objective 1784.0000000

Root relaxation: objective 1.797000e+03, 4 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1797.0000000 1797.00000  0.00%     -    0s

Explored 1 nodes (4 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 1797 1784 1563 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=24
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x473ac067
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 1571.0000000
Presolve removed 3265 rows and 3267 columns
Presolve time: 0.00s
Presolved: 40 rows, 65 columns, 170 nonzeros
Variable types: 0 continuous, 65 integer (64 binary)
Found heuristic solution: objective 1797.0000000

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1797 1571 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=25
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xd00fda1f
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 1646.0000000
Presolve removed 3275 rows and 3281 columns
Presolve time: 0.00s
Presolved: 30 rows, 51 columns, 117 nonzeros
Variable types: 0 continuous, 51 integer (48 binary)
Found heuristic solution: objective 1797.0000000

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 1797 1646 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=26
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x83d3e292
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective 1762.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 1797 1762 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=27
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x1af93551
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective 1762.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 1797 1762 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image 
=================== for P=28
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xaa492b11
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective 1797.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 1: 1797 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
No description has been provided for this image
No description has been provided for this image

Task: Repeat the whole process with another fishnet_points with different fishnet interval.¶

In [61]:
from shapely.geometry import Point

# Here, we are going to create fishnet points.
    # Fishnet points are points spaced with an equal interval.
    # You'll see when you see the output!

# Define the interval between points 
#### Note: Adjust interval value as needed for lab question 2
def create_fishnet(interval):
# Create arrays of x and y coordinates using np.arange
    x_coords = np.arange(minx, maxx, interval)
    y_coords = np.arange(miny, maxy, interval)

    # Create a list to store the points
    fishnet_points = []

    # Generate points for the fishnet
    for y in y_coords:
        for x in x_coords:
            fishnet_points.append((x, y))

    # Print the number of points generated
    print("Number of points in the fishnet:", len(fishnet_points))

    fishnet_points = gpd.GeoSeries([Point(pt_cd) for pt_cd in fishnet_points])
    fishnet_points = fishnet_points[fishnet_points.within(SBC_FD.geometry[0])].reset_index()
    fishnet_points.plot(figsize=(15,5))
    return fishnet_points

interval = 5280/2  # default: 5280/5 feet (1 mile / 5 = 0.2 mile) 
fishnet_points = create_fishnet(interval)

Number of points in the fishnet: 1290
No description has been provided for this image
In [62]:
current_coverage = fishnet_points.within(stations.buffer(S).unary_union).sum()

fishnet_points["weight"] = 1

I = len(fishnet_points)
J = len(stations)
a_i = fishnet_points["weight"]

D_ij = [[np.sqrt((fishnet_points.geometry.x[i] - stations.geometry.x[j])**2 + (fishnet_points.geometry.y[i] - stations.geometry.y[j])**2)
         for j in range(J)] for i in range (I)]

N_i = [[j for j in range(len(D_ij[0])) if D_ij[i][j] <= 8000]
       for i in range (len(D_ij))]
In [67]:
optimize_and_evaluate(demand_block=False)

=================== for P=3
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xcef4b780
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective 13.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 43.0000000

Root relaxation: objective 8.600000e+01, 39 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0      86.0000000   86.00000  0.00%     -    0s

Explored 1 nodes (39 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 86 43 13 

Optimal solution found (tolerance 1.00e-04)
Best objective 8.600000000000e+01, best bound 8.600000000000e+01, gap 0.0000%
No description has been provided for this image 
=================== for P=4
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x6c1b8065
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective 13.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 67.0000000

Root relaxation: objective 1.130000e+02, 35 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     113.0000000  113.00000  0.00%     -    0s

Explored 1 nodes (35 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 113 67 13 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.130000000000e+02, best bound 1.130000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=5
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x0edd7bb0
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective 39.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 86.0000000

Root relaxation: objective 1.380000e+02, 33 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     138.0000000  138.00000  0.00%     -    0s

Explored 1 nodes (33 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 138 86 39 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.380000000000e+02, best bound 1.380000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=6
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x7ec0d3f0
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective 64.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 111.0000000

Root relaxation: objective 1.610000e+02, 35 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     161.0000000  161.00000  0.00%     -    0s

Explored 1 nodes (35 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 161 111 64 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.610000000000e+02, best bound 1.610000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=7
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xc0c56a2c
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective 67.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 114.0000000

Root relaxation: objective 1.840000e+02, 29 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     184.0000000  184.00000  0.00%     -    0s

Explored 1 nodes (29 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 184 114 67 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.840000000000e+02, best bound 1.840000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=8
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x42f51dea
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective 95.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 138.0000000

Root relaxation: objective 2.040000e+02, 22 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     204.0000000  204.00000  0.00%     -    0s

Explored 1 nodes (22 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 204 138 95 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.040000000000e+02, best bound 2.040000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=9
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xa05648d8
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective 119.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 169.0000000

Root relaxation: objective 2.210000e+02, 26 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     221.0000000  221.00000  0.00%     -    0s

Explored 1 nodes (26 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 221 169 119 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.210000000000e+02, best bound 2.210000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=10
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x9694b029
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 119.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 182.0000000

Root relaxation: objective 2.360000e+02, 22 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     236.0000000  236.00000  0.00%     -    0s

Explored 1 nodes (22 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 236 182 119 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.360000000000e+02, best bound 2.360000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=11
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x53e70d3e
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 120.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 208.0000000

Root relaxation: objective 2.480000e+02, 23 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     248.0000000  248.00000  0.00%     -    0s

Explored 1 nodes (23 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 248 208 120 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.480000000000e+02, best bound 2.480000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=12
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xde16faa2
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 131.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 212.0000000

Root relaxation: objective 2.600000e+02, 20 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     260.0000000  260.00000  0.00%     -    0s

Explored 1 nodes (20 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 260 212 131 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.600000000000e+02, best bound 2.600000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=13
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x2e87b538
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 144.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 221.0000000

Root relaxation: objective 2.710000e+02, 14 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     271.0000000  271.00000  0.00%     -    0s

Explored 1 nodes (14 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 271 221 144 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.710000000000e+02, best bound 2.710000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=14
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xe773f88b
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective 161.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 244.0000000

Root relaxation: objective 2.750000e+02, 13 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     275.0000000  275.00000  0.00%     -    0s

Explored 1 nodes (13 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 275 244 161 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.750000000000e+02, best bound 2.750000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=15
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xf376824c
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 188.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 255.0000000

Root relaxation: objective 2.780000e+02, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     278.0000000  278.00000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 278 255 188 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.780000000000e+02, best bound 2.780000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=16
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x34bf2713
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 200.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 268.0000000

Root relaxation: objective 2.800000e+02, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     280.0000000  280.00000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 280 268 200 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.800000000000e+02, best bound 2.800000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=17
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x2fae766a
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 201.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 271.0000000

Root relaxation: objective 2.820000e+02, 9 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     282.0000000  282.00000  0.00%     -    0s

Explored 1 nodes (9 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 282 271 201 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.820000000000e+02, best bound 2.820000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=18
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xaef0dd05
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 201.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 271.0000000

Root relaxation: objective 2.830000e+02, 4 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     283.0000000  283.00000  0.00%     -    0s

Explored 1 nodes (4 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 283 271 201 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=19
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xeb12e722
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 202.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 270.0000000

Root relaxation: objective 2.830000e+02, 5 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     283.0000000  283.00000  0.00%     -    0s

Explored 1 nodes (5 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 283 270 202 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=20
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xdcf615d7
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 217.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 281.0000000

Root relaxation: objective 2.830000e+02, 5 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     283.0000000  283.00000  0.00%     -    0s

Explored 1 nodes (5 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 283 281 217 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=21
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xbec14725
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 217.0000000
Presolve removed 485 rows and 488 columns
Presolve time: 0.00s
Presolved: 34 rows, 58 columns, 151 nonzeros
Variable types: 0 continuous, 58 integer (56 binary)
Found heuristic solution: objective 282.0000000

Root relaxation: objective 2.830000e+02, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     283.0000000  283.00000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 283 282 217 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=22
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x7000900b
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 243.0000000
Presolve removed 487 rows and 491 columns
Presolve time: 0.00s
Presolved: 32 rows, 55 columns, 137 nonzeros
Variable types: 0 continuous, 55 integer (52 binary)
Found heuristic solution: objective 282.0000000

Root relaxation: objective 2.830000e+02, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     283.0000000  283.00000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 283 282 243 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=23
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x6558704c
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 243.0000000
Presolve removed 488 rows and 493 columns
Presolve time: 0.00s
Presolved: 31 rows, 53 columns, 130 nonzeros
Variable types: 0 continuous, 53 integer (50 binary)
Found heuristic solution: objective 282.0000000

Root relaxation: objective 2.830000e+02, 5 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     283.0000000  283.00000  0.00%     -    0s

Explored 1 nodes (5 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 283 282 243 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=24
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x2ed23144
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 244.0000000
Presolve removed 490 rows and 496 columns
Presolve time: 0.00s
Presolved: 29 rows, 50 columns, 119 nonzeros
Variable types: 0 continuous, 50 integer (47 binary)
Found heuristic solution: objective 283.0000000

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 8 (of 8 available processors)

Solution count 2: 283 244 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=25
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x4c00ff32
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective 257.0000000
Presolve removed 519 rows and 546 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 283 257 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=26
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xd21c0cfb
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective 277.0000000
Presolve removed 519 rows and 546 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 283 277 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=27
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0x9811cf51
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective 277.0000000
Presolve removed 519 rows and 546 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 2: 283 277 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image 
=================== for P=28
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (mac64[arm] - Darwin 22.1.0 22A400)

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 519 rows, 546 columns and 1103 nonzeros
Model fingerprint: 0xae7d1ec3
Variable types: 0 continuous, 546 integer (546 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective 283.0000000
Presolve removed 519 rows and 546 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 8 available processors)

Solution count 1: 283 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.830000000000e+02, best bound 2.830000000000e+02, gap 0.0000%
No description has been provided for this image
No description has been provided for this image

Question 10: Compare the Scatter plots out of Blocks, 0.2 mile fishnet points, and another fishnet points with interval of your choice. Discuss the insights you can get. ( 5 pts )¶

In Lab 2, we discovered that different Coverage Distance Standard can impact the coverage analysis result.
In Lab 4, we can discover how different demand representation makes difference.
Share your insights about

  • provide three scatter plots ( 3 pts )
  • how SBC_FD is currently doing with existing stations in terms of coverage ( 1 pt )
  • how demand representation impacts the coverage analysis ( 1 pt )

TIP: you can copy and paste your screenshot into markdown cells

PUT your answer HERE Screenshot 2024-05-24 at 9.32.21 AM.png ... Screenshot 2024-05-24 at 9.31.01 AM.png Screenshot 2024-05-24 at 9.31.54 AM.png

... SBC_FD is currently doing pretty well with theie existing stations in terms of coverage, as they are covering 167619 people with 28 stations. The demand being represented by fishnet points of 0.2 miles, the results show that about 180000 people can be covered which would be better than the current coverage. However, this is likely to take a lot of investment and resources, so may be practically unreasonable. Nevertheless, this would only be about a 7 percent increase in coverage, so may not be worth the efforts. In addition, when the demand is represented by 0.5 mile fishnet points, only about 300 people are covered.The scatterplots also show that the same coverage results can be obtained using only about 18 stations, as the scatterplot plateaus around there.

...